In this work we will analyze the distribution of the energies of the protons that could have produced neutrinos with a given observed energy (in the TeV–PeV range). This is in particular useful to understand what are the CR energies being probed with the observed astrophysical neutrinos. We will also discuss the resulting shape of the spectra of the neutrinos for the different scenarios. We will base the study on the analytical fits to the neutrino yields that parametrize the results of numerical simulations obtained in [1]}, based on the SIBYLL 2.1 model [2]} to account for the \(pp\)  hadronic interactions, and in [3]}, relying on the SOPHIA code [4]} to account for the \(p\gamma \)  interactions. Further studies of the photon spectra in \(pp\)  interactions were performed in [5]}, and the neutrino and photon spectra resulting in some post-LHC models were considered in [6]}, obtaining results which are essentially consistent with those we will adopt from [1]}, [3]}.
